Following the GBM [1]} framework, the \(K\)  functions in Eq. (REF ) are learned additively to minimize the objective in Eq. (REF ).
With some transformation and simplification (see details in [2]}), the \(s\) -th tree is learned by minimizing the following objective \(\tilde{\mathcal {L}}^{(s)}\)  as
\(\small \tilde{\mathcal {L}}^{(s)}=\sum _{i=1}^n \Big [g_i f_s(\mathbf {x}_i)+\frac{1}{2}h_i f_s^2(\mathbf {x}_i)\Big ]+\Omega (f_s),\nonumber \\g_i=\frac{\partial l(y_i,\hat{y_i}^{(s-1)})}{\partial \hat{y_i}^{(s-1)}},\ \ h_i=\frac{\partial ^2l(y_i,\hat{y_i}^{(s-1)})}{\partial (\hat{y_i}^{(s-1)})^2}\nonumber ,\) 
